ON CERTAIN DEGENERATE ONE-PHASE FREE BOUNDARY PROBLEMS

被引：4
作者：
De Silva, Daniela [1 ]
Savin, Ovidiu [1 ]
机构：
[1] Columbia Univ, Barnard Coll, Dept Math, New York, NY 10027 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2021年 / 53卷 / 01期
关键词：
free boundary problems; regularity; viscosity solutions; ELLIPTIC-EQUATIONS; REGULARITY;
D O I：
10.1137/19M1308128
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more generally for minimizers of the Alt-Phillips functional.
引用
收藏
页码：649 / 680
页数：32
相关论文
共 15 条
[1]  
ALT HW, 1981, J REINE ANGEW MATH, V325, P105
[2]  
ALT HW, 1986, J REINE ANGEW MATH, V368, P63
[3]  
Caffarelli L., 1987, Rev. Mat. Iberoam., V3, P139
[4]  
Caffarelli L, 1988, Ann. Scuola Norm. Sup. Pisa., V15, P583
[5]  
Caffarelli L. A., 1995, Fully nonlinear elliptic equations, V43
[6]   A HARNACK INEQUALITY APPROACH TO THE REGULARITY OF FREE BOUNDARIES .2. FLAT FREE BOUNDARIES ARE LIPSCHITZ [J].
CAFFARELLI, LA .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (01) :55-78
[7]   The obstacle problem revisited [J].
Caffarelli, LA .
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1998, 4 (4-5) :383-402
[8]   REGULARITY OF FREE BOUNDARIES IN HIGHER DIMENSIONS [J].
CAFFARELLI, LA .
ACTA MATHEMATICA, 1977, 139 (3-4) :155-184
[9]   QUASI-HARNACK INEQUALITY [J].
De Silva, D. ;
Savin, O. .
AMERICAN JOURNAL OF MATHEMATICS, 2021, 143 (01) :307-331
[10]   Free boundary regularity for a problem with right hand side [J].
De Silva, D. .
INTERFACES AND FREE BOUNDARIES, 2011, 13 (02) :223-238
12